Best weighted L∞ approximate preinverses of fuzzy matrices with max-min composition

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-04-15 DOI:10.1016/j.fss.2025.109417

Yan-Kuen Wu , Ching-Feng Wen , Zhaowen Li , Hsun-Chih Kuo

引用次数: 0

Abstract

An efficient solution procedure for the preinverse (or postinverse) of a fuzzy matrix is useful for solving the well known problems of fuzzy abductive/backward reasoning. Wen, Wu and Li (2023) have presented algebraic formulas for various approximate preinverses of fuzzy matrices using the weighted

L_{1}

norm. In this study, a novel approach is proposed to derive the best approximate preinverses of fuzzy matrices, in the sense that the weighted

L_{\infty}

norm of residual error is minimized. The proposed approach requires only simple arithmetic operations, it is possible to perform real-time abductive reasoning in many reasoning systems such as intelligent diagnosis.

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具有最大-最小构成的模糊矩阵的最佳加权 L∞ 近似前推

模糊矩阵前逆（或后逆）的高效求解程序有助于解决众所周知的模糊归纳/反向推理问题。Wen、Wu 和 Li (2023) 利用加权 L1 准则提出了各种模糊矩阵近似前逆的代数公式。在本研究中，提出了一种新方法来推导模糊矩阵的最佳近似前推，即加权 L∞ 准则的残差误差最小。所提出的方法只需要简单的算术运算，就可以在智能诊断等许多推理系统中进行实时归纳推理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.